864 Appendix IL be investigated, as examples of slider-crank and quadriocrank chains respectively. Fig. 826 is the linkwork of an oscillating engine, where CP is the crank and BP the piston rod, and the ratio w of CP to wj. of B P is required. Linear velocity of P, normally to c P = #, and normally to B P = v^ Now if i) = s P, v-^=s T, and sr ^ = = x T5T> BP ST B P But by similar triangles ST SP sr v B P S P BP OP BP # . BP OP Again, Produce Also draw- d v = wj o P z> = w x rad. = a) c P 6U - CP = o^ -OP B p to F, and draw G F at right angles to B F. G F || c P, making triangles B F G, B p c similar. > OP BP B c ~ = = = >! C P P F C G or, if B c be angular velocity of crank, c G- is that of piston rod Then, if c G be turned round to g, a point is found in a polar curve of angular velocity of B p when w is constant. In the quadric crank, Fig. 827, let o be the virtual centre. Then w. A P = zi, and o^ B Q = \. Draw AL || B Q, making triangles o P Q and A P L similar. Also produce Q P to s, making triangles SAL and SBQ similar. Finally o> AP or v AP OP 1 OQ BQ A P AL _ AP AL .BQ " AI, BS A~S If the chain be that of a beam engine, w is constant and represented by B Q, while ^ is shewn by A L. Turn A L round on to line A p and a point I is found in a polar curve which shews uj-i for any position of crank A p. P.502. Efficiency of Transruissian by Shafting, The